3.1.5.14. Concrete02IS Material (Concrete02 with Initial Stiffness Control)

This command is used to construct a uniaxial concrete material with the same compressive envelope and tension/cyclic behavior as Concrete02 Material – Linear Tension Softening, but with user-defined initial stiffness E₀. In Concrete02 the initial stiffness is fixed at $E_c = 2f'_c/\varepsilon_{c0}$; Concrete02IS allows any E₀ (e.g. $57000\sqrt{f'_c}$ or secant stiffness to peak).

uniaxialMaterial Concrete02IS $matTag $E0 $fpc $epsc0 $fpcu $epsU <$lambda $ft $Ets>

Argument	Type	Description
$matTag	integer	unique material tag
$E0	float	initial (elastic) stiffness
$fpc	float	concrete compressive strength at 28 days (compression negative)
$epsc0	float	concrete strain at maximum strength (negative)
$fpcu	float	concrete crushing strength (negative)
$epsU	float	concrete strain at crushing strength (negative)
$lambda	float	(optional) ratio between unloading slope at epsU and initial slope
$ft	float	(optional) tensile strength
$Ets	float	(optional) tension softening stiffness (absolute value)

Note

Compressive parameters (fpc, epsc0, fpcu, epsU) are taken as negative; if given positive, they are converted to negative internally. The input E₀ affects the unloading/reloading stiffness in compression. The ascending branch uses the Popovics equation (Concrete02 uses the Hognestad parabola).

Example

Tcl Code

set fc 4000.0
set epsc0 -0.002
set fcu -1000.0
set epscu -0.006
# Same initial stiffness as Concrete02
set Ec [expr 2.0*$fc/(-$epsc0)]
uniaxialMaterial Concrete02IS 1 $Ec $fc $epsc0 $fcu $epscu
# With tension and optional parameters
uniaxialMaterial Concrete02IS 2 $Ec $fc $epsc0 $fcu $epscu 0.1 500.0 1738.33

Python Code

fc, epsc0 = 4000.0, -0.002
fcu, epscu = -1000.0, -0.006
Ec = 2.0 * fc / (-epsc0)
ops.uniaxialMaterial('Concrete02IS', 1, Ec, fc, epsc0, fcu, epscu)
ops.uniaxialMaterial('Concrete02IS', 2, Ec, fc, epsc0, fcu, epscu, 0.1, 500.0, 1738.33)